Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40M7 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&40\\59&113\end{bmatrix}$, $\begin{bmatrix}3&80\\50&51\end{bmatrix}$, $\begin{bmatrix}13&100\\91&111\end{bmatrix}$, $\begin{bmatrix}43&40\\107&51\end{bmatrix}$, $\begin{bmatrix}119&40\\115&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.7.dvr.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $8$ |
Cyclic 120-torsion field degree: | $256$ |
Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.144.3-40.bw.1.4 | $40$ | $2$ | $2$ | $3$ | $1$ |
60.144.3-60.ff.1.1 | $60$ | $2$ | $2$ | $3$ | $1$ |
120.48.0-120.dg.1.8 | $120$ | $6$ | $6$ | $0$ | $?$ |
120.144.3-40.bw.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-60.ff.1.17 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.byg.1.35 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.byg.1.56 | $120$ | $2$ | $2$ | $3$ | $?$ |